Simplifying (2x^4y^7)^3
This expression involves the power of a product and requires careful application of exponent rules. Let's break down the process stepbystep.
Understanding the Exponent Rules
 Power of a product: (ab)^n = a^n * b^n
 Power of a power: (a^m)^n = a^(m*n)
Applying the Rules

Distribute the exponent: Since we have a product (2x^4y^7) raised to the power of 3, we can apply the power of a product rule. This gives us:
(2x^4y^7)^3 = 2^3 * (x^4)^3 * (y^7)^3

Simplify the powers: Now we apply the power of a power rule to each individual term:
2^3 * (x^4)^3 * (y^7)^3 = 8 * x^(43) * y^(73)

Final result: This simplifies to:
8 * x^(43) * y^(73) = 8x^12y^21
Conclusion
Therefore, the simplified form of (2x^4y^7)^3 is 8x^12y^21.